DT EC 02: Lateral torsional buckling – constant

Description

Geometry	Cross-section:	70x221mm
Geometry	Material:	C24
Load	ULS FC:	5.37kNm
Standard		EN 1995-1-1 [- -]
Design parameters	k_mod: L_LT:	0.8 3m

Independent reference results

Open handcalculations

The effective beam length $L_{eff}$ is given in Table 6.1 from EN 1995-1.

$\begin{align*} L_{eff}&= 0.9 \cdot L +2 \cdot h \\ &= 0.9 \cdot 3 \text{m} +2 \cdot 0.221 \text{m} \\ &= 3.14 \text{m} \\ L_{eff}&= \frac{L}{C_1} +2 \cdot h \text{ general case}\\ \end{align*}$

Diamonds uses a factor 0.9 because there’s a uniform load on the beam. Although Diamonds assumes the loads act in the shear center, $+ 2 \cdot h$ is always added to $L_{eff}$ to take into account that loads might act in the compression zone.
For deviating load distrutions and boundary conditions this method Serna, Lopez, Puente and Young is used to determine $C_1$ . The 0.9 for a uniform load corresponds to a $C_1=\frac{1}{0.9}=1.11$ .
The user can also impose C₁ via .

Next we determine the critical bending stress $\sigma_{m.crit}$ :

(6.31) $\begin{align*} \sigma_{m.crit}&=\frac{0.78 \cdot b^2 \cdot E_{0.05}}{h \cdot L_{ef}} \\ &=\frac{0.78 \cdot \left(70 \text{mm}\right)^2 \cdot 7370 \text{MPa}}{0.221 \text{m} \cdot 3.14 \text{m}}\\ &=40.57 \text{MPa} \end{align*}$

The relative slenderness for bending $\overline{\lambda_{m}}$ :

(6.30) $\begin{align*} \overline{\lambda_{m}}&=\sqrt{\frac{f_{m.k}}{\sigma_{m.crit}}} \\ &=\sqrt{\frac{24 \text{MPa}}{40.57 \text{MPa}}}\\ &=0.77 \end{align*}$

Factor for the reduced bending strength $k_{crit}$ :

(6.34) $\begin{align*} k_{crit}&=1.56 - 0.75 \cdot \overline{\lambda_{m}} \\ &=1.56 -0.75 \cdot 0.77\\ &=0.98 \end{align*}$

The unity check UC:

(6.35) $\begin{align*} M_{y.Rd}&=W_y \cdot f_{m.d}\\ &=569812 \text{mm³} \cdot \frac{k_{mod} \cdot f_{m.k}}{\gamma_m}\\ &=569812 \text{mm³} \cdot \frac{0.8 \cdot 24 \text{MPa}}{1.3}\\ &=8.4 \text{kNm}\\ UC&=\left( \frac{M_{Ed}}{k_{crit} \cdot M_{Rd}} \right)^2 + \frac{N_{c.Ed}}{k_{c.z} \cdot N_{Rd}}\\ &=\left( \frac{5.37 \text{kNm}}{0.98 \cdot 8.4 \text{kNm}} \right)^2 + 0\\ &= 64.91 \% \end{align*}$

Diamonds results and comparison

Stability verification of the beam according to EN 1995-1-1

Intermediate results in Diamonds for lateral torsional buckling

Results	Independent reference	Diamonds	Difference
$L_{eff}$	3.14m	3.14m	0,00%
$\sigma_{m.crit}$	40.57MPa	40.57MPa	0,00%
$\overline{\lambda_{m}}$	0.77	0.77	0,00%
$k_{crit}$	0.98	0.98	0,00%
Unity check	64.91%	64.91%	0,00%

References

Tested in Diamonds 2025.

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